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Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

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Abstract

In this paper, a hybrid projection algorithm for a countable family of mappings is considered in Banach spaces. The sequence generated by algorithm converges strongly to the common fixed point of the mappings. We apply the result for the resolvent of a maximal monotone operator for finding a zero of it, which is a solution of the equilibrium problem. The results obtained extend the research in this context, such as the corresponding results of Aoyama et al. (Nonlinear Anal 71(12):1626–1632, 2009, nonlinear analysis and optimization, Yokohama Publishers, Yokohama, pp. 1–17, 2009), Solodov et al. (Math Program 87(1):189–202, 2000), Ohsawa et al. (Arch Math 81(4):439–445, 2003) and Kamimura et al. (SIAM J Optim 13(3):938–945, 2002).

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Acknowledgements

The authors are thankful to the two anonymous reviewers for their suggestions, which helped us to improve the quality of the article. We are deeply indebted to the editor, for his step-by-step advices. Vahid Dadashi is supported by the Islamic Azad University–Sari Branch.

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Authors and Affiliations

  1. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

    Vahid Dadashi

  2. China Medical University, Taichung, Taiwan

    Mihai Postolache

  3. University Politehnica of Bucharest, Bucharest, Romania

    Mihai Postolache

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  1. Vahid Dadashi
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  2. Mihai Postolache
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Correspondence to Mihai Postolache.

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Dadashi, V., Postolache, M. Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming. J Optim Theory Appl 174, 518–529 (2017). https://doi.org/10.1007/s10957-017-1117-0

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  • DOI: https://doi.org/10.1007/s10957-017-1117-0

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